Fact-Checked and Approved by: David Chen, CFA, Quantitative Analyst.
The Poker Variance Calculator helps players quantify the impact of short-term luck (or unluck) on their observed win rate, providing a confidence interval for their true expected profitability (EV).
Poker Variance Calculator
True Win Rate Confidence Interval (95%):
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Detailed Calculation Steps:
Run the calculation to see the steps…
Poker Variance Calculator Formula
The calculation determines the Confidence Interval (CI) for a player’s true long-term Win Rate based on their sample size and standard deviation (variance measure).
CI = Observed Win Rate ± Margin of Error (ME)
ME = Z-Score * (Standard Deviation / sqrt(Hands in Hundreds))
Formula Sources: PokerVariance.com Explanation | TwoPlusTwo Magazine Article
Variables Explained
To accurately calculate the confidence interval, the following inputs are required:
- Observed Win Rate (BB/100): Your current actual profitability, measured in Big Blinds won or lost per 100 hands played.
- Standard Deviation (BB/100): A measure of how widely your results fluctuate from hand to hand. This is the core measure of volatility in your game. Higher SD means higher variance.
- Total Hands Played: The size of your sample. The larger the sample, the narrower the confidence interval will be.
- Confidence Level (%): The probability that your true long-term win rate falls within the calculated interval. Common levels are 95% (Z=1.96) or 99% (Z=2.576).
What is Poker Variance?
Variance in poker refers to the short-term fluctuations in results that are caused purely by chance, rather than skill. Because poker has elements of hidden information and random card distribution, even highly skilled players can experience significant losing streaks (downswings) or winning streaks (upswings) that do not accurately reflect their true long-term expected value (EV).
Understanding variance is crucial for bankroll management. A player with a high win rate but also a high standard deviation (meaning a volatile style of play) will require a much larger bankroll to weather potential downswings compared to a similarly winning but less volatile player.
This calculator quantifies the range where your *true* win rate is likely to be, separating the signal (skill) from the noise (luck) based on your sample size.
How to Calculate Poker Variance (Example)
Let’s use an example to illustrate the process:
- Input Data: Assume a player has an Observed Win Rate of 5 BB/100, a Standard Deviation of 80 BB/100, and has played 50,000 hands. We set the Confidence Level to 95% (Z = 1.96).
- Convert Hands to Hundreds: The formula requires the sample size in hundreds. 50,000 Hands / 100 = 500.
- Calculate Standard Error: Divide the Standard Deviation by the square root of Hands in Hundreds: $80 / \sqrt{500} \approx 80 / 22.36 \approx 3.577$.
- Calculate Margin of Error (ME): Multiply the Standard Error by the Z-Score: $ME = 1.96 \cdot 3.577 \approx 7.011$.
- Determine the Interval:
- Lower Bound: $5 – 7.011 = -2.011 \text{ BB/100}$
- Upper Bound: $5 + 7.011 = 12.011 \text{ BB/100}$
Result: We are 95% confident that the player’s true long-term win rate is between -2.011 BB/100 and 12.011 BB/100. This wide range demonstrates the massive impact of variance over 50k hands.
Frequently Asked Questions (FAQ)
How many hands do I need to determine my true win rate?
There is no magic number, but for the confidence interval to shrink to a truly useful range, samples of 200,000 hands or more are generally recommended. Until then, variance will always be a major factor.
Is a higher Standard Deviation always bad?
Not necessarily. While high SD means more volatility, it often correlates with a highly aggressive, high-risk/high-reward style. If you have a high win rate along with a high SD, you might still be a great player, but you will need a bigger bankroll.
What is BB/100?
BB/100 is the standard metric for measuring poker profitability, standing for Big Blinds won or lost per 100 hands played. This normalizes results across different stake levels.
What is the difference between variance and bankroll management?
Variance is the *statistical phenomenon* of short-term deviation from the long-term expected value. Bankroll management is the *strategy* of maintaining sufficient funds to survive the negative consequences (downswings) caused by variance.